The Klein-Gordon Equation and Differential Substitutions of the Form $v=\phi (u,u_x,u_y)$

Abstract

We present the complete classification of equations of the form $u_{xy}=f(u,u_x,u_y)$ and the Klein-Gordon equations $v_{xy}=F(v)$ connected with one another by differential substitutions $v=\phi (u,u_x,u_y)$ such that ${\phi }_{u_x}{\phi }_{u_y}\ne 0$ over the ring of complex-valued variables.

References in corpus (1)

• New exact solutions of nonlinear variants of the RLW, the PHI-four and Boussinesq equations based on modified extended direct algebraic method

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